1. Field of the Invention
This invention relates to digitally implemented modulators which are employed to provide a bandlimiting function upon a binary input sequence.
2. Description of the Prior Art
Digitally implemented modulators are illustrated in the article, "Microprocessor implementation of high-speed modems", IEEE Trans Commun. Vol. COM-25, Feb. 1977. For example, they may comprise a coder for converting a binary input sequence, of a predetermined length, representing a series of symbols, into two output pulse trains by a coding rule. The two output pulse trains of the coder are then applied to respective, identical, digital finite impulse response low-pass filters. The outputs of the filters are a pair of signals which are modulated by a pair of respective digital modulators. The modulators multiply the filter outputs by samples of sine and cosine signals. The resulting products are summed to yield the digital output of the modulator. This gives a suitable modulated analog signal for transmission after digital-to-analog conversion and simple low-pass filtering.
The above article discloses a microprocessor implementation of a digital transversal filter. ROM is used to store the filter coefficients and RAM is used to store input samples for multiplication by the coefficients. The microprocessor provides the necessary multiplication and addition functions to provide a filtered output signal.
A known method for simplifying the multiplication step is to store, in a look-up table, all possible outputs of the modulator. The input symbols are used to address the look-up table to provide the modulated output. To implement a digital filter using this look-up table approach, a software model, running on a large computer, is used to generate the required output samples for all possible combinations of input symbols. Because the look-up table must be finite in extent, the filter responses to given inputs must also be finite. This naturally leads to the use of the Finite Impulse Response (FIR) type of digital filter which meets this requirement.
This type of FIR filter may be visualized as a tapped delay line, employing a series of shift registers coupled together and having output "taps" for outputting data stored in each shift register. To keep the look-up table as small as possible, the number of taps must be kept as small as possible. Design analysis shows that 25 taps is about the minimum number which will give the required performance for both passband and stopband filters. Additionally, to keep the look-up table size down, the sampling rate used by the filter must be kept as low as possible. The limiting factor is the Nyquist criterion, in which the sampling rate must be at least twice the maximum frequency handled by the filter. The present invention provides for a maximum frequency of about 3 kHz.
The size of a look up table required for a digital filter representing a tapped delay line having 25 taps, a sampling frequency of 7.2 kHz, a Nyquist frequency of 3.6 kHz and a baud rate of 600 Hz can be calculated mathematically. Given that 600 symbols are processed per second (baud rate of 600 Hz), 12 output samples are required for each symbol, and the filter will be working on the data from 3 input symbols at any one time, the calculations are as follows: (1) Each symbol is represented by a 4 bit binary number, thus giving 16 possible inputs to the filter; (2) 3 symbols are processed at one time, therefore, the filter processes 16.times.16.times.16 combinations of inputs, or 4096 combinations, each represented by an 8 bit byte, and (3) there are 12 samples to be stored for each of these, so 12.times.4096 or 49,152 bytes of storage are required. This equates to 393,216 bits of storage. Since the modem of the present invention uses two distinct frequency bands to transmit on, two such tables are required, so that 98,304 bytes, or 786,432 bits of storage are required to implement a complete set of tables for the transmitter. This represents a large storage requirement for a small system such as a modem.
By contrast, the present invention generates final modulated waveforms by using a look-up table in which samples of components of such waveforms are stored, and in which, 3 numbers taken from the look-up table are added together, the sum being the current output sample.